$\tau$-tilting finiteness of two-point algebras I

TL;DR

This paper classifies $ au$-tilting finite two-point algebras, focusing on minimal wild and some tame cases, advancing understanding of their algebraic properties.

Contribution

It provides the first classification of $ au$-tilting finiteness for two-point algebras, including minimal wild and certain tame cases.

Findings

Identified $ au$-tilting finiteness for minimal wild two-point algebras

Determined $ au$-tilting finiteness for some tame two-point algebras

Established foundational results for future classification studies

Abstract

As the first attempt to classify $\tau$-tilting finite two-point algebras, we have determined the $\tau$-tilting finiteness for minimal wild two-point algebras and some tame two-point algebras.